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Prove that following : 2 sin^-1 x = co...

Prove that following :
`2 sin^-1 x = cos^-1 (1-2x^2), 0 le x le 1`

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PRADEEP PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. Find the value of cos^-1(sqrt3/2) + 2 sin^-1(sqrt3/2)

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  2. Find the value of sin^-1[cos(sin^-1(sqrt3/2))]

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  3. Prove that following : 2 sin^-1 x = cos^-1 (1-2x^2), 0 le x le 1

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  4. Prove the following: 3sin^–1 x = sin^–1 (3x – 4x^3), x in [–1/2 , 1/2]

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  5. Prove the following: 3cos^–1 x = cos^–1 (4x^3 – 3x), x in [1/2,1]

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  6. Prove that following : cos^-1 x = 2 sin^-1 sqrt(1-x)/(2) = 2cos^-1 s...

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  7. Prove that following : sin(2 cos^-1(-4/5)) = - (24/25)

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  8. Prove that following : cos(2sin^-1(-2/5)) = 17/25

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  9. Prove that following : cos(3cos^-1(2/5)) = - (118)/(125)

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  10. Write the following functions in the simplest form: sin^-1 sqrt(1-x^...

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  11. Write the following functions in the simplest form: cos^-1 sqrt(1-x^...

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  12. Write the following functions in the simplest form: cos^-1 (2x^2 - 1...

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  13. Write the following functions in the simplest form: cos^-1 (1-2x^2),...

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  14. Find x if cos(sin^-1 (1/5) + os^-1 x) = 0

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  15. Find x if sin^-1(8/x) + sin^-1 (15/x) = pi/2

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  16. Find x if cos^-1 x + sin^-1 (x/2) = pi/6

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  17. Find x if sin^-1 x + sin^-1 (1-x) = cos^-1 x

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  18. Find x if sin^-1 (6x) + sin^-1 (6sqrt3x) = - pi/2

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  19. Prove that : sin^-1 (-4/5) = cos^-1 (-3/5) - pi

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  20. Prove that : sin^-1(3/5) + sin^-1(8/17) = sin^-1(77/85)

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